Determine the reactions and draw the shear and bending moment diagrams for the structur...

Compute the degrees of indeterminacy:

Total number of reactions of the given beam is, but we have only three equilibrium equations,

Therefore degree of indeterminacy of the beam is given by

Primary beam:

Obtained by removing the hinged support A from the given indeterminate beam

Primary beam subjected to external loading

Here, denotes the horizontal deflection and denotes the vertical deflection at A due to external loading

Therefore from virtual work method,

And

Primary beam subjected to unit value of the redundant

Here, anddenotes the deflection at AX and AY due to unit value of the redundant

Therefore, from virtual work method

And

Primary beam subjected to unit value of the redundant

Here, anddenotes the deflection at AY and AX due to unit value of the redundant

Therefore from virtual work, we get

And

Compatibility equation:

The compatibility equation can be expressed as

By substituting the obtained values into the compatibility equation (1) and (2),determine the redundantand

Solve the equations (1) and (2).

Draw the free body diagram of the frame:

Compute the reactions of the beam:

Apply equilibrium equations:

Therefore, the horizontal reaction at E is .

Compute the vertical reaction at E.

Therefore, the vertical reaction at E is .

Compute the bending moment at E.

Therefore, the bending moment at E is .

Draw the bending moment diagrams.